N−3 azide anion confined inside finite-size carbon nanotubes

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N–3 azide anion confined inside finite-size carbon nanotubes

Stefano Battaglia, Stefano Evangelisti, Noelia Faginas Lago, Thierry Leininger

To cite this version:

Stefano Battaglia, Stefano Evangelisti, Noelia Faginas Lago, Thierry Leininger. N–3 azide anion con-

fined inside finite-size carbon nanotubes. Journal of Molecular Modeling, Springer Verlag (Germany),

2017, 23 (10), pp.294. �10.1007/s00894-017-3468-8�. �hal-01657201�

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Accepted Manuscript

The final publication is available at link.springer.com at the following link:

https://link.springer.com/article/10.1007%2Fs00894-017-3468-8

DOI: https://doi.org/10.1007/s00894-017-3468-8

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(will be inserted by the editor)

N

⁻

3

Azide Anion Confined Inside Finite-Size Carbon Nanotubes

Stefano Battaglia · Stefano Evangelisti · Noelia Faginas-Lago · Thierry Leininger

Received: date / Accepted: date

Stefano Battaglia

Laboratoire de Chimie et Physique Quantiques, IRSAMC, Universit´e Paul Sabatier, 118 Route de Narbonne, F-31062 Toulouse Cedex - France

Dipartimento di Chimica, Biologia e Biotecnologie, Universit`a degli Studi di Perugia, Vie Elce di Sotto 8, I-06123 Perugia, Italy

Stefano Evangelisti

Noelia Faginas-Lago

Dipartimento di Chimica, Biologia e Biotecnologie, Universit`a degli Studi di Perugia, Vie Elce di Sotto 8, I-06123 Perugia, Italy

Thierry Leininger

Tel.: +33 (0)5 61 55 61 52

E-mail: [email protected]

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Abstract

In this work, the conﬁnement of an N

⁻₃

azide anion inside finite-size single-wall zigzag and armchair carbon nanotubes of different diameters has been studied by wave function and density functional theory. Unrelaxed and relaxed interaction energies have been computed, resulting in a favorable interaction be- tween the guest and host system. In particular, the largest interaction has been observed for the confinement in an armchair (5

,

5) carbon nanotube, for which a natural population analysis as well as an investigation based on the molecular elec- trostatic potential has been carried out. The nature of the interaction between the two fragments appears to be mainly electrostatic, favored by the enhanced polariz- ability of the nanotube wall treated as a ﬁnite system and passivated by hydrogen atoms. The results obtained are promising for possible applications of this complex as a starting point for the stabilization of larger polynitrogen compounds, suitable as a high-energy density material.

Keywords

Carbon Nanotubes

^·

HEDM

^·

Polynitrogen Compound

^·

Azide Anion

^·

Molecular Conﬁnement

1 Introduction

In the search for alternative energy sources and environmentally friendly fuels, polynitrogen compounds (PNCs) exhibit a high potential of success due to the amount of energy released by their decomposition into inert N

2

molecules and they have thus been proposed as possible high-energy density material (HEDM)[1, 2].

Among them, probably the most famous one is the N

⁻₃

azide anion known since the

end of the nineteenth century[3], which has regained much attention after the suc-

cessful synthesis of the N

⁺₅

cation[4], envisioning the pure nitrogen salt N

⁻₃

N

⁺₅

[5,

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6, 7, 8]. Considering PNCs as HEDM, the illustrative example of the energy stored in the ionic cluster N

⁻₃

N

⁺₅

is emblematic, where upon dissociation into four N

2

molecules, the release of energy is around 70 kcal/mol per mole of N

2

[7].

Despite the eﬀorts, the main diﬃculty still remains the intrinsic instability of PNCs, which at ambient conditions mostly dissociate into N

2

directly or overcom- ing a low energy barrier. A recently proposed approach predicted the stabilization of an N

8

chain through molecular conﬁnement inside carbon nanotubes (CNTs)[9, 10], for which it has been shown that the polymeric nitrogen form is stable at ambient conditions when it resides inside the nanotube cavity. Additional stud- ies considering several N

8

chains conﬁned in a carbon nanotube bundle and the conﬁnement inside boron nitride nanotubes have obtained similar results[11, 12].

Experimentally, it has been possible to stabilize an N

⁻8

anionic species on multi- wall CNTs at ambient conditions, although not with the goal of energy storage[13].

A comprehensive theoretical study by density functional theory (DFT) on nitrogen clusters with diﬀerent number of atoms encapsulated in a C

60

fullerene has been carried out too, predicting stable structures up to 13 atoms before starting to be incorporated in the conﬁning cage[14]. Conﬁnement inside carbon nanostructures has not been explored only for PNCs, but for other types of molecular clusters too; most notably for Ga

ⁿ

and Al

ⁿ

clusters, for which increased stabilization and new isomers have been found for the encapsulated species[15, 16].

The success of this approach has led us to this contribution, in which we propose

to conﬁne the simplest nitrogen compound beyond N

2

, the N

⁻₃

azide anion, inside

single-wall ﬁnite-size carbon nanotubes of diﬀerent diameters. From a theoretical

perspective, using

^ab-initio

molecular orbital theory, we investigate the eﬀects of

the encapsulation by computing (un-)relaxed interaction energies using both den-

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sity functional theory (DFT) and wave function theory (WFT) and we study the the effects on both the guest nitrogen species and the host carbon structure by means of atomic charges and molecular electrostatic potentials (MEPs). The arti- cle is organized as follows. In the Computational Details Section we describe the methodology used to perform the calculations, in the Results Section we show the results obtained in this study and at last, in the Conclusions Section we finalize this work by summarizing and highlighting the most important findings.

2 Computational Details

In this work, single-wall carbon nanotubes have been treated as ﬁnite-size systems, passivated on both edges by the addition of one hydrogen atom for each terminal carbon atom. Two classes of CNTs have been considered, namely (

n

,0) zigzag and (

m

,

m

) armchair CNTs, with values of

n

equal to 8, 10 and 12, and values of

m

equal to 4, 5 and 6. The length of the tubes was of

^≈

13

.

57 ˚ A for (

n

,0) CNTs and

≈

15

.

43 ˚ A for (

m

,

m

) CNTs. The geometries of both types have been relaxed using restricted density functional theory using the three-parameter Becke exchange energy functional[17, 18] and the Lee-Yang-Parr correlation energy functional[19]

(RB3LYP), optimizing the lowest energy state at this level of theory (triplet state

for zigzag CNTs and singlet state for armchair CNTs). Similarly, the trinitrogen

anion has also been optimized using RB3LYP. The basis set used for all calculations

is the double-

ζ

6-31G basis set[20], with the addition of polarization and diﬀuse

functions (6-31+G*) on the nitrogen atoms. Note that polarization functions on

the carbon atoms do not aﬀect qualitatively the results (with errors within

^≈

2

.

5 kcal/mol) and therefore they were not included in the systematic calculations

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carried out in this work.

The interaction energy has been calculated in two ways, listed as follows

Eint^unrel

=

Etot−Ecnt−E_N− 3

,

(1)

Eint^rel

= ˜

Etot−_E

˜

cnt−_E

˜

N⁻₃ ,

(2)

where the presence of a tilde means that the single point calculation has been per- formed on the geometry obtained by relaxing the entire system, and its absence implies that the geometries used were optimized for the single fragments alone.

The basis set superposition error has been taken into account by the counterpoise correction procedure by Boys and Bernardi[21].

The total and fragment energies have been computed with second-order

n

-electron valence perturbation theory (NEVPT2) on top of a complete active space self- consistent ﬁeld (CASSCF) calculation in the case of zigzag CNTs, and with second- order Møller-Plesset perturbation theory (MP2) in the case of armchair nanotubes.

The reason behind the application of diﬀerent methodologies is the open-shell

character of the ground state of (

n

,0) nanotubes, which requires a multirefer-

ence approach in order to properly account for the

^static

correlation eﬀects. To

compute relaxed interaction interaction energies, the systems involving armchair

nanotubes have been relaxed using DFT with the dispersion-corrected APFD

exchange-correlation energy functional[22], which best reproduced the MP2 un-

relaxed interaction energies. The results obtained on the fully relaxed structures

have been computed using both DFT and MP2 perturbation theory. All calcula-

tions involving zigzag nanotubes have been performed using the 2015.1 version of

the MOLPRO program package[23, 24] and applying, while all those involving arm-

chair nanotubes with the Gaussian09 suite of programs[25] and the built-in NBO

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program[26]. The calculations using Gaussian09 have been performed setting the

“Integral” option to “Ultraﬁne”. The ﬁgures appearing in this article have been produced using either the avogadro program version 1.2.0[27, 28], or GaussView version 5[29].

3 Results

At ﬁrst, unrelaxed interaction energies have been computed by placing the N

⁻₃

ion exactly in the center of the nanotube (i.e. the center of the

xy

-plane cutting the nanotube), aligned to its principal axis and with the central nitrogen atom in the nanotube midpoint (see Fig. 1). The resulting energies for CNTs of diﬀerent dimensions and classes are depicted in Fig. 2. For all diameters considered, the interaction is favorable (i.e negative) and thus the nanotube has a stabilizing ef- fect on the conﬁned N

⁻₃

ion. Although the computational methods employed for the two classes of nanotubes are not the same, the interaction energy “smoothly”

varies with respect to the diameter suggesting that the nanotube class does not aﬀect signiﬁcantly the interaction between the guest and the host system. This result is of particular interest since it implies that the structural pattern of the nanotube wall does not play a role for this kind of “weak” interactions.

The strongest stabilization is found for CNTs with a diameter comprised between

6

.

26 ˚ A and 6

.

78 ˚ A, with interaction energies of about

^{≈ −}

31 kcal/mol. A small

(6

,

0) CNT was tested too (diameter of 4

.

70 ˚ A), but the positive interaction energy

of more than 100 kcal/mol clearly indicated that the cavity is too small to host

the N

⁻₃

fragment. Nanotubes larger than the (12

,

0) one were not considered since

the behavior of the interaction energy appears clear. In theory, by keeping the

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N

⁻₃

molecule ﬁxed at the center of the nanotube while increasing its diameter, the interaction energy should decrease and approach zero when the CNT wall is so far away that the nitrogen ion does not feel their inﬂuence anymore.

The (5

,

5) CNT has the largest stabilizing eﬀect and thus for this case the full sys- tem has been relaxed using restricted DFT with APFD functional. The geometry optimization has been started from 6 diﬀerent orientations of the N

⁻₃

moiety inside the nanotube as depicted in Fig. 3, in order to ensure that the system does not fall into a too high local minimum. The geometry of Fig. 3a is the same used in the unrelaxed calculation, and upon optimization the position of N

⁻₃

remains virtually unchanged. The relaxation of starting geometries depicted from Fig. 3b to Fig. 3d yields ﬁnal structures similar to that of Fig. 3a, where the anion is in the center of the nanotube, slightly displaced from its midpoint along the principal axis. In geometries shown in Figs. 3e and 3f, the N

⁻₃

moiety was initially displaced towards one end of the nanotube besides being rotated and moved closer to the wall as in the previous cases. Interestingly, also in this latter case the relaxed structures are very similar to the previous ones; during optimization the N

⁻₃

ion moves towards the midpoint of the nanotube instead of remaining near the edge (see Fig. 4).

Each relaxed geometry is diﬀerent. In all cases the N

⁻₃

fragment lies almost per- fectly in the center of the CNT, with deviations of at most 0

.

03 ˚ A from the princi- pal axis. In contrast, its relative position along the axis varies much more among the obtained geometries and in the extremest case the central nitrogen atom is displaced by 0

.

43 ˚ A from the midpoint of the CNT. Despite these diﬀerences in the relaxed structures, energetically they lie all very close to each other, with a maximum diﬀerence of merely 0

.

05 kcal/mol.

It is possible that the geometry relaxation induces considerable changes in the

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interaction energy of diﬀerent nanotubes than the (5

,

5) CNT, therefore systems involving a (4

,

4) CNT and a (6

,

6) CNT have been relaxed too, starting from a single geometry similar to the one depicted in Fig. 3f. For the small (4

,

4) CNT, the ﬁnal position of the anion is in the center of the nanotube parallel to the principal axis, displaced by 0

.

7 ˚ A towards one end of it. In the case of the (6

,

6) CNT, because of the considerably larger cavity, the N

⁻₃

fragment attracted to the nanotube wall moves out of the principal axis and stabilize itself at a distance of

≈

3

.

10 ˚ A, remaining parallel too it (see Fig. 5).

For these two geometries and the lowest-energy conformation involving the (5

,

5) CNT, relaxed MP2 interaction energies have been computed and compared to the APFD results, as it is shown in Fig. 6. The energies obtained with the diﬀerent methods agree very well, with the largest diﬀerence of

^≈

2

.

60 kcal/mol obtained for the (4

,

4) CNT. The comparison with the unrelaxed interaction energies also shows a good agreement; the best interaction (at MP2 level of theory) is main- tained by the (5

,

5) CNT, slightly decreasing from

⁻

31

.

12 kcal/mol to

⁻

32

.

31 kcal/mol, whereas for the other two nanotubes it decreases by

^≈

2

.

5 kcal/mol.

Thus, the relaxation process does not change qualitatively the results obtained

for the unrelaxed structures. Most likely, one can expect the relaxation to aﬀect

more nanotubes with a large diameter, since by ﬁxing the N

⁻₃

ion in the center of

the nanotube would quickly decrease the interaction energy to zero as the diame-

ter increases, while allowing for structural relaxation would give the N

⁻₃

fragment

the freedom to be absorbed on the inner side of the nanotube wall, attaining the

interaction energy of an N

⁻₃

ion absorbed on a graphene sheet in the limit of an

inﬁnitely large CNT. It is interesting to note that the distance from the N

⁻₃

ion

to the (5

,

5) CNT wall ranges between 3

.

45 ˚ A and 3

.

50 ˚ A, which is slightly more

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than the optimal absorption distance measured for the (6

,

6) CNT, i.e.

^≈

3

.

10 ˚ A.

The nanotube has virtually no inﬂuence on the geometry of the N

⁻₃

ion; it remains perfectly linear and its bond length decreases by only 0

.

001 ˚ A for all starting ge- ometries, whereas the deformation energy observed never exceeds 0

.

01 kcal/mol.

In a similar way, the CNT distortion due to the presence of N

⁻₃

has been quantiﬁed to be to at most 0

.

4 kcal/mol.

The charge distribution on the N

⁻₃

ion is also minimally aﬀected by the pres- ence of the nanotube. Partial atomic charges on the nitrogen monomer have been computed through a natural population analysis[30] for the simple system in gas phase and for the full complex. The analysis for the monomer shows an excess of 0

.

14 positive charge on the central nitrogen atom, and an accumulation of nega- tive charge equal to

⁻

0

.

57 on the two external nitrogen atoms. This distribution changes weakly after relaxation of the complex system, with the partial charge on the central atom decreasing to 0

.

12 and increasing to

⁻

0

.

55 on the two exter- nal nitrogen atoms (see Fig. 7). Of particular interest are the electrostatic eﬀects induced by the presence of the negatively charged species inside the nanotube cavity. In this respect, the partial atomic charges on the nanotube change sign in the region of the N

⁻₃

moiety. The molecular electrostatic potential (MEP) of the nanotube electron density has been plotted for the isolated system and compared to the MEP obtained with the electron density inﬂuenced by the host fragment.

The MEP depicted in Fig. 8a has been computed from the ground state electron

density of the nanotube alone. One can clearly see the polarization at both ends

of the nanotube due to the passivation of the system with hydrogen atoms. The

positive charge accumulated at the edges is balanced by an excess of negative

charge distributed on the carbon atoms, mostly on the atoms directly bonded to

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the hydrogens (this is also supported by the NPA, which attributes positive partial charges of 0

.

26 on each H atom and negative partial charges of

⁻

0

.

22 on each con- nected C atom). The MEP shown in Fig. 8b has been obtained from the diﬀerence of the total system electron density and the N

⁻3

electron density computed in the basis of the total system, allowing us to appreciate the effect of the anion on the CNT charge distribution. In the central region of the nanotube, around the posi- tion of the anion, the charge of the nanotube flips sign and becomes positive. This is particularly evident from the bottom plot of Fig. 8b showing the value of the electrostatic potential inside the cavity. The sign flip does not occur everywhere, the carbon atoms at the edges remain negatively charged suggesting why during the geometry relaxation the N

⁻₃

ion moved back to the midpoint of the nanotube.

The positively charged hydrogens are shielded by the carbon atoms, making the CNT edge to eﬀectively appear neutral to the N

⁻₃

fragment, which tends to go to the midpoint of the nanotube where it can be most easily polarized.

We argue that the stabilization of the N

⁻₃

moiety in the CNT cavity is largely

due to electrostatic interactions. The conﬁned ion induces a polarization on the

nanotube, favored by the hydrogen passivation at both ends, causing a redistri-

bution of the charge on the CNT wall such that the N

⁻₃

fragment does not leave

the cavity. Moreover, the diameter of the (5

,

5) CNT is such that the conﬁned

N

⁻3

azide anion lies at an optimal absorption distance from the wall surrounding

it (in all directions), which makes it the most favorable host system among the

nanotubes considered.

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4 Conclusions & Outlook

In this work we have studied the confinement of the azide anion inside finite-size single-wall zigzag and armchair CNTs of different diameters. It has been found that the N

⁻₃

anion is stabilized by nanotubes of diameters comprised between

^≈

5

.

5 ˚ A and

^≈

9

.

5 ˚ A, with the most favorable interaction energy of

⁻

32

.

31 kcal/mol been obtained for a (5

,

5) CNT with a diameter of

^≈

6

.

78 ˚ A. The analysis of the relaxed structures, the natural atomic charges and the molecular electrostatic potential has revealed the possible nature of the interaction, suggesting an explanation of the results found. In particular, we argue that the guest N

⁻₃

molecule is stabilized by electrostatic interactions with the nanotube wall, undergoing a remarkable po- larization catalyzed by the passivation of the nanotube edges through hydrogen atoms. The (5

,

5) CNT allows the N

⁻₃

fragment to perfectly align itself in the center of the nanotube at an optimal distance from its wall in all directions, thus making it the best host system.

Although the N

⁻₃

azide anion is one of the most stable PNCs, the results obtained in this contribution are promising in the context of alternative energy storage and HEDM as an intermediate step toward the stabilization of more complex species which are energetically more appealing. In this moment, work is in progress in order to study the behavior of N

5

ionic species, N

⁻5

and N

⁺5

respectively, if they are placed in ﬁnite-size CNTs. The case of the cation is particularly interesting, since this almost linear molecule could be, in principle, hosted in CNTs similarly to the linear N

⁻₃

.

Preliminary results of this ionic species show a favorable unrelaxed interaction en-

ergy in the same order of magnitude as for the N

⁻₃

moiety, whereas the relaxation

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process poses in this case some complications due to the high electron aﬃnity of the cation. Indeed, it has been observed a considerable charge transfer from the nanotube wall to the nitrogen compound, altering signiﬁcantly the N

⁺₅

geometry, eventually leading to an undesired breaking of the molecule.

In order to avoid an excessive charge transfer from the CNT to the PNC, an an- ionic species could be inserted together with the N

⁺₅

fragment. The existence of an ionic solid formed by N

⁻₃

and N

⁺₅

species has been subject to several theoretical studies, all predicting a low probability of success. Nonetheless, the recent the- oretical ﬁndings of a stable polymeric N

8

chain inside carbon and boron nitride nanotubes and stable N

ⁿ

clusters inside a fullerene have suggested a new way to form stable polynitrogen compounds.

In particular, this approach could open the possibility to perform a reaction of the type N

⁻₃

+ N

⁺₅ ^→

N

8

inside the nanotube, allowing the stabilization of more complex PNCs which does not directly dissociate to nitrogen molecules.

5 Acknowledgments

This work has been funded by the European Union’s Horizon 2020 research and in- novation programme under the Marie Sk lodowska-Curie grant agreement n

^o

642294.

The calculations of this contribution have been performed under the grant 2016-

p1048 at the HPC center CALMIP and the local computing cluster of the Lab-

oratoire de Physique et Chimie Quantiques of Toulouse. N. F.-L. acknowledges

ﬁnancial support from Fondazione Cassa di Risparmio di Perugia (P 2014/1255,

ACT 2014/6167). Finally, the authors wish to thank O. Brea for her contributions

to the graphical material.

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(a) (b)

Fig. 1 Example geometry of N⁻₃ confined inside a (5,5) CNT used to compute unrelaxed interaction energies

−40

−35

−30

−25

−20

−15

−10

−5 0

5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 (4,4)

(8,0) (5,5)

(10,0)

(6,6) (12,0)

Interactionenergy(kcal/mol)

Tube diameter (˚A) MP2 NEVPT2

Fig. 2 Unrelaxed interaction energies

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(a)

(d)

(b)

(e)

(c)

(f)

Fig. 3 Starting orientations of N⁻₃ inside a (5,5) CNT prior the geometry relaxation. In the last two cases (e) and (f), the N⁻₃ ion is closer to the edge of the CNT, while in all other cases is placed in the midpoint

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(a) (b) Fig. 4 Starting (a) and final (b) position of the N⁻₃ ion inside the CNT

Fig. 5 Relaxed geometry of N⁻3 confined inside a (6,6) CNT

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−40

−35

−30

−25

−20

−15

−10

−5 0

5 5.5 6 6.5 7 7.5 8 8.5 9

(4,4)

(5,5)

(6,6)

Interactionenergy(kcal/mol)

Tube diameter (˚A) MP2 APFD

Fig. 6 Relaxed interaction energies

−0.57 +0.14 −0.57

(a)

−0.55 +0.12 −0.55

(b)

Fig. 7 Partial atomic charges for the N⁻₃ fragment outside (a) and inside a (5,5) CNT (b)

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+9.41

−9.41

(a) (b)

Fig. 8 Electrostatic potential map of the (5,5) CNT unperturbed (a) and perturbed by the presence of the N⁻₃ molecule (b). Isosurface value of the electron density set to 0.02 and energy scale given in kcal/mol